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The Bacteriologist Problem - part 1

A scientist is experimenting with bacteria that are one micron in diameter and that reproduce by dividing every minute into two bacteria. At 12:00 PM, she puts a single organism in a container. At precisely 1:00 PM, the container is full.

At what time was the container half full?

The container was half full at 12:59 PM. When the bacteria doubled in the next minute, the container became full. This is an example of exponential growth where the growth rate is a mathematical function that is proportional to the function's current value.

Reader Brian Clark submitted the following comment:

I arrived at the "correct" solution of 12:59 pm for the beaker being half full but I knew that it was still wrong because bacteria need nutrients so the beaker could not be empty to begin with. Bacteria do not reproduce using only air or vacuum. Also the beaker would attain mass from nothing as the microbes filled the beaker which is impossible. Even supposing the beaker was filled to the brim with nutrients and you look at it as only the bacteria "filling the beaker" you are still assuming that the bacteria will have perfect nutrient-to-bacterial-volume conversion in the beaker which is also not likely although I am not a biochemist. Comments?

Brian is correct. The law of conservation of mass states that the mass in a closed isolated system will remain constant over time, i.e., matter cannot be created nor destroyed. This problem is an exercise in mathematics and logical thinking. The bacteriologist problem does not represent a model of a real system, but it is more precisely defined mathematically than the riddle:

Woodchuck
How much wood would a woodchuck chuck if a woodchuck could chuck wood?